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Question Number 192925 by Shrinava last updated on 31/May/23

$$\mathrm{Find}:\mathrm{x}=?$$$$1.2^{\mathbf{x}+1}+0,5^{\mathbf{x}-2}=9$$$$2.4^{3\mathbf{x}}=12$$$$3.6^{\mathbf{x}+2}=18$$

Answered by MM42 last updated on 31/May/23

$$1)2\times 2^x+4\times 2^{-x}=9$$$$2^x=u\Rightarrow 2u^2-9u+4=0$$$$u=\frac{9\pm 7}{4}\Rightarrow 2^x=4\Rightarrow x=2\mathrm{\&}{2}^x=0.5\Rightarrow x=-1$$$$2)3x={log}_{4}12=1+{log}_{4}3\Rightarrow x=\frac{1}{3}+\frac{1}{3}{log}_{4}3$$$$4)x+2={log}_{6}18=1+{log}_{6}3\Rightarrow x=-1+{log}_{6}3$$$$$$

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